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The purpose of this paper is to study the time average behavior of Markovchains with transition probabilities being kernels of completely continuousoperators, and therefore to provide a sufficient condition for a class ofMarkov chains that are frequently used in dynamic economic models to beergodic. The paper reviews the time average convergence of the quasi-weaklycomplete continuity Markov operators to a unique projection operator. Also, itshows that a further assumption of quasi-strongly complete continuity reducesthe dependence of the unique invariant measure on its corresponding initialdistribution through ergodic decomposition, and therefore guarantees the Markovchain to be ergodic up to multiplication of constant coefficients. Moreover, asufficient and practical condition is provided for the ergodicity in economicstate Markov chains that are induced by exogenous random shocks and acorrespondence between the exogenous space and the state space.

Operator-Theoretical Treatment of Ergodic Theorem and Its Application to Dynamic Models in Economics